The widely used Stanford-Binet IQ test has a mean of 100 points and standard dev

Question

The widely used Stanford-Binet IQ test has a mean of 100 points and standard deviation of 15 points. Assume that the population of IQ scores on this test are normally distributed.

a. The minimum score for entry into Mensa, a group for people with high IQs, is 138. Determine the proportion of this population who are eligible to join Mensa.

Round your answer to four decimal places.

b. Another high-IQ group known as the Triple Nine Society requires an IQ score at or above the 99.9th percentile, so that only the top .1% of IQ scores in the population are eligible. Determine the minimum IQ score required to join the Triple Nine Society.

Round your answer to one decimal place.

c. Marilyn vos Savant, author of the "Ask Marilyn" column in Parade magazine, is reported to have an IQ score of 228. How many standard deviations above the mean is this?

Round your answer to two decimal places.

Explanation / Answer

Mean is 100 and SD=15

A. P(x>138)= P(z>(138-100)/15)=P(z>2.53)

Or 1-P(z<2.53) from normal distribution table gives 1-0.9943= 0.0057

B. Z for 0.999 probability is 3.09

Therefore (x-100)/15=3.09

Or x= 146.35

C. We need to find z=(228-100)/15

Or z= 8.53

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.